范德瓦尔登数研究

Some Results on Van Der Waerden Number

将范德瓦尔问题推广成圆周上的范德瓦尔登问题及其等价的不等式组(线性不定方程组),并求出了(各个子不等式组)局部的解数公式Sp(k)及其上、下界公式.

In this paper, we translate the van der Waerden number problem into the van der Waerden number problem on circle, and we find the equivalent form Sp （ k ） of its inequality. At the same time, we also obtain formula of local system of inequality, especially we obtain the lower and upper bounds of Sp （ k ）.